Sandy, I think maybe the multiple meanings of the word "sprouting" have confused you. The seed in a seed mix are, by definition, varied, so what grows ("sprouts") depends on what each seed came from. You might be able to grow millet, for instance, which, when mature, might (depending on your climate and that type millet's needs) yield more millet seed in a few months. Some of the seed in the mix might yield edible greens. But what a circuitous way to get greens!
What I do instead is plant the greens I want for my birds, ones I know like my climate, and at a time of year that's good for growing them. This season I've grown collards, Swiss chard, arugula, dandelions, broccoli, kale, and spinach. Since your climate is the same as mine, unless you have quite an impressive light set-up for indoor gardening, your chances of getting seed to grow anything edible over the winter are slim to none IMHO.
If you use covered jars to "sprout" selected seed, you can feed them to your bird as sprouted seed in 24-72 hrs.
http://www.landofvos.com/articles/wbsprouts.html Sprouting decreases the fat in the seed significantly, making sprouted seed far more nutritious for your bird than dry seed. I recommend you try that.